> Why some kinds of information processing and not others?

Consciousness isn't something the information processing has, it is something the information processing does. It's a function, not some magic property that happens on top.

Consciousness is simply your brains ability to figure out what part of all the sensory input it gets can be attributed to the "self", just like other parts might be labeled as cats, dogs, table and chairs, some will be labeled as self.

And I am sure one day somebody will boil that down to some nice math, since fundamentally it's about networks. If the brain wants to move a hand from one spot to another, that's easy if it is its own hand, a couple of nerve impulses and it will happen. If that hand belongs to somebody else, moving it is a whole different ballgame. That fundamental different in connectedness should be expressible.